Answer 1:
In order to answer your question we are going
to make some assumptions until we build to the
final answer.
If the Earth were perfectly
spherical, not rotating, and had no interactions
with the sun or the moon, then the force of
gravity on an object would be the same everywhere
on the earth's surface using Newton's Law of
Gravitation. Newton's Law says that the force of
gravity is equal to a gravitational constant (G)
times the product of the two masses (M and m)
divided by the distance between the centers of
mass for both objects (r) squared. Mathematically
this relation looks like
F = G M m /r^{2}.
But since the Earth is rotating,the radius of
the Earth is larger near the equator than near the
poles, so the force of gravity at the equator
would be less than at the poles. If you add into
this situation the effect of tides caused by the
moon and sun, the difference can become a little
larger.
We can calculate what this difference
would be. Let's call the equatorial radius
6378140 m, and the polar radius 6356752 m
(check this out at the following site):
Earth radius .
Using a gravitational constant
of 6.67*10^{11}
Nm^{2}/kg^{2}, and a mass of the
earth of 6*10^{24} kg, let's calculate
the gravitational force on a 70 kg (about 155 lbs)
person at both the equator and the poles.
At the equator the force of gravitational
attraction is 689 N. At the poles the force of
gravitational attraction is 693 N.
So, even though there is a difference
gravity, it is not noticeable to humans since the
difference is about half a percent.
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